For starters, you'd likely need to increase your savings in a big way. While saving 15 to 25 percent per paycheck is recommended to be able to retire at 67, you'll need to increase that to around 50 percent to retire by 40, Kimmie Greene, money expert at Intuit and spokeswoman for Mint.com, tells CNBC Make It.

However, even if putting half of your paycheck in the bank each month is feasible, it's not the enough to guarantee a successful early retirement plan.

"It really depends on not only what your salary is and what your living expenses are, but also where else you'll be getting potential income from," Greene says. "Do you receive a bonus as part of your job? Do you receive stock options?" Any large lump sum can provide a jump-start to your savings.

Planning for an early retirement should start in your 20s and take into account lifestyle factors, such as where you live and your industry. Do you want to live in San Francisco? Or work for a non-profit? Those dreams might not jibe with financial independence.

While there are exceptions to every rule, you'll give yourself the best shot at early retirement by choosing to live somewhere relatively cheap and aiming to work in a lucrative industry.

Once you're committed to the idea of saving half your income and giving financial independence a shot, you need to save and re-invest your money so that it grows as quickly as possible.

"You're probably going to want to be a little bit riskier in your investments than the average person so your money can work as hard for you as possible and you can potentially outpace that average six, seven, eight percent that people get as a return on investment in the stock market," Greene says.

Traditional retirement savings vehicles, such as 401(k)s and IRAs, have penalties for withdrawing money before you turn 59-and-a-half, so varying your investments is crucial. Greene recommends online tools such as Acorns, which allows users to invest their spare change, and Fundrise, which pairs users up with real estate developers.

Greene also points out that if early retirement is your No. 1 priority, other financial goals, such as paying off your student loans, might need to be put on the back-burner.

"If it can earn six to eight percent in the market, as opposed to paying down a student loan that has a pretty low interest rate, you're going to want to put it in an alternative [investment] that has a higher growth rate," Greene says.

The takeaway here is that, if you want to retire early, your savings account alone won't allow you to reach that goal. But putting away 50 percent of your paycheck each month is a good place to start.